Observational Constraints on Cosmology from the Modified Friedmann Equation

Recent measurements of type Ia supernovae as well as other concordant observations suggest that the expansion of our universe is accelerating. A dark energy component has usually been invoked as the most feasible mechanism for the acceleration. However, the effects arising from possible extra dimensions can mimic well the role of a dark energy through a modified Friedmann equation. In this work, we investigate some observational constraints on a scenario in which this modification is given by H 2 = 8πG 3 (ρ + Cρn). We mainly focus our attention on the constraints from recent measurements of the dimensionless coordinate distances to type Ia supernovae and Fanaroff-Riley type IIb radio galaxies compiled by Daly and Djorgovski (2003) and the X-ray gas mass fractions in clusters of galaxies published by Allen et al. (2002,2003). We obtain the confidence region on the power index n of the modificative term and the density parameter Ωm of the universe from a combined analysis of these databases. It is found that n = 0.06 +0.22 −0.18 and Ωm = 0.30 +0.02 −0.02, at the 95.4 % confidence level, which is consistent within the errors with the standard ΛCDM model. These parameter ranges give a universe whose expansion swithes from deceleration to acceleration at a redshift between 0.52 to 0.73. – 2 – Subject headings: cosmological parameters — cosmology: theory — distance scale — supernovae: general — radio galaxies: general — X-ray: galaxies:clusters 1.